# ---
# title: 1021. Remove Outermost Parentheses
# id: problem1021
# author: Tian Jun
# date: 2020-10-31
# difficulty: Easy
# categories: Stack
# link: <https://leetcode.com/problems/remove-outermost-parentheses/description/>
# hidden: true
# ---
# 
# A valid parentheses string is either empty `("")`, `"(" + A + ")"`, or `A +
# B`, where `A` and `B` are valid parentheses strings, and `+` represents string
# concatenation.  For example, `""`, `"()"`, `"(())()"`, and `"(()(()))"` are
# all valid parentheses strings.
# 
# A valid parentheses string `S` is **primitive** if it is nonempty, and there
# does not exist a way to split it into `S = A+B`, with `A` and `B` nonempty
# valid parentheses strings.
# 
# Given a valid parentheses string `S`, consider its primitive decomposition: `S
# = P_1 + P_2 + ... + P_k`, where `P_i` are primitive valid parentheses strings.
# 
# Return `S` after removing the outermost parentheses of every primitive string
# in the primitive decomposition of `S`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: "(()())(())"
#     Output: "()()()"
#     Explanation:
#     The input string is "(()())(())", with primitive decomposition "(()())" + "(())".
#     After removing outer parentheses of each part, this is "()()" + "()" = "()()()".
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: "(()())(())(()(()))"
#     Output: "()()()()(())"
#     Explanation:
#     The input string is "(()())(())(()(()))", with primitive decomposition "(()())" + "(())" + "(()(()))".
#     After removing outer parentheses of each part, this is "()()" + "()" + "()(())" = "()()()()(())".
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: "()()"
#     Output: ""
#     Explanation:
#     The input string is "()()", with primitive decomposition "()" + "()".
#     After removing outer parentheses of each part, this is "" + "" = "".
#     
# 
# 
# 
# **Note:**
# 
#   1. `S.length <= 10000`
#   2. `S[i]` is `"("` or `")"`
#   3. `S` is a valid parentheses string
# 
# 
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
